A repunit is a number consisting solely of ones (such as 11 or 11111).
Let us call p(n) a 10-base integer represented by a string of n ones, e.g. p(1)=1, p(5)=11111 etc.
Most of the repunit numbers are composite.
2, 19,23,317 are the first four indices of prime repunits.

Prove: For a prime repunit p(n) to be prime, n has to be prime.

(In reply to Another proof by Gamer)

The "proof " errs:

yoo wrongly defined  q

In your example just exchange x and y ,you get 111*101,clearly

not p(6)

Edited on January 11, 2011, 2:53 am

Posted by Ady TZIDON on 2011-01-11 02:10:16